whizzing sounds (sometimes) when turning the A/C on

Hi,
recently I experienced the following issue when turning on the A/C in my Honda Accord '94 (~100,000 miles). There is some whizzing sound like when fan makes some noise.
It doesn't always come up when I turn the A/C on, but it usually stops when I turn it off. Sometimes (more rarely) I noticed that this noise comes up even with the A/C off.
I had my mechanic check it today and he told me that the cooling fan motor bearings are getting bad so they need to be replaced. Could this be related to the A/C? Also, might there be an additional fan that is getting bad?
TIA michael
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